The performance of fibre-optic transmission systems is affected by amplifier noise and transmission impairments, such as Chromatic Dispersion (CD), Polarization Mode Dispersion (PMD), and non-linear effects. Transmission impairments become more relevant as the bit-rate increases. The compensation, or mitigation, of transmission impairments by electronic processing in direct-detection systems is not simple and may be ineffective because of the information loss caused by direct-detection. On the other hand, in coherent systems, all linear impairments such as CD or PMD could be exactly compensated by electronic equalisers. The use of coherent systems with electronic processing at the receiver also allows for reducing the symbol-rate by deploying efficient multilevel modulation formats, such as DQPSK and QAM, which are more resilient to CD and PMD. In addition, phase, frequency, and polarization locking of local oscillators, previously required in coherent receivers, can be conveniently substituted by electronic post-processing. For these reasons, coherent systems have been recently proposed again as a promising solution for next generation high-capacity fibre-optic links.
Techniques are known for equalisation of signals to compensate for impairments during transmission. These techniques include linear equalization based on feed forward equalisers (FFE), decision feedback equalisers (DFE), maximum likelihood sequence detection (MLSD), and Non-linear Tapped Delay Line (TDL) equalisers based on Volterra kernels. Most solutions of electronic processing/equalisation in fibre-optic systems refer to the mitigation of linear impairments (CD and PMD) in direct detection systems by means of FFE+DFE (H. Bulow and G. Thielecke, “Electronic PMD mitigation—From linear equalization to maximum-likelihood detection,” in Proc. OFC, 2001, vol. 3, pp. WDD34-1-WDD34-3), MLSD (T. Foggi, E. Forestieri, G. Colavolpe, and G. Prati, “Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD,” J. Lightwave Technol., vol. 24, no. 8, pp. 3073-3087, August 2006), or non-linear TDL (C. Xia, and W. Rosenkranz “Nonlinear electrical equalization for different modulation formats with optical filtering,” J. Lightwave Technol., vol. 25, no. 4, April 2007). Recently, the exact compensation of linear impairments in coherent systems by means of FFE has been investigated and some MLSD strategies for the exact compensation of linear impairments in systems with differential detectors have been also proposed.
High transmission bit-rates (e.g. ≧40 Gbit/s) require high-speed digital processing. Computational cost is a driving factor and it is desirable that the complexity of an equaliser in transmission equipment is kept as low as possible. Linear equalisers, such as FFE, are not able to compensate for non-linear impairments and so have a limited effectiveness, while MLSD has a high complexity (exponential with channel memory). Proper metrics and suitable channel estimation techniques for the non-linear fibre-optic channel are still unknown. Non-linear TDL equalisers based on Volterra kernels have a high complexity (exponential with non-linearity order).